A bead of mass `m` slides without friction on a vertical hoop of radius `R`. The bead moves under the combined influence of gravity and a spring of spring constant `k` attached to the bottom of the hoop. For simplicity assume, the equilibrium length of the spring to be zero. The bead is released at the top of the hoop with negligible speed as shown . The bead, on passing the bottom point will have a velocity of `:`

A bead of mass m can slide without friction on a fixed circular horizontal ring of radius 3R having a centre at the point C. The bead is attached to one of the ends of spring of spring constant k. Natural length of spring is R and the other end of the spring is R and the other end of the spring is fixed at point O as shown in the figure. If the bead is released from position A, then the kinetic energy of the bead when it reaches point B is

A bead of mass m can slide without friction on a fixed circular horizontal ring of radius 3R having a centre at the point C. The bead is attached to one of the ends of spring of spring constant k. Natural length of spring is R and the other end of the spring is R and the other end of the spring is fixed at point O as shown in the figure. If the bead is released from position A, then the kinetic energy of the bead when it reaches point B is

A bead of mass m can slide without friction along a vertical ring of radius R. One end of a spring of force constant k=(3mg)/(R ) is connected to the bead and the other end is fixed at the centre of the ring. Initially, the bead is at the point A and due to a small push it starts sliding down the ring. If the bead momentarily loses contact with the ring at the instant when the spring makes an angle 60^(@) with the vertical, then the natural length of the spring is

A bead of mass m can slide without friction along a vertical ring of radius R. One end of a spring of force constant k=(3mg)/(R ) is connected to the bead and the other end is fixed at the centre of the ring. Initially, the bead is at the point A and due to a small push it starts sliding down the ring. If the bead momentarily loses contact with the ring at the instant when the spring makes an angle 60^(@) with the vertical, then the natural length of the spring is

A bead of mass 'm' is attached to one end of a spring of natural length R & spring constant k = ((sqrt3 + 1))/(R) . The other end of the spring is fixed at point A on a smooth vertical ring of radius R as shown. The normal reaction at B just after it is released to move is

A head slide without friction around a loop the (figure). The bead slide is released is from rest at a height h = 3.50R . How large is the normal force on the bead at point (A) if its mass is 50 g ?

A bead of mass m moves on a rod without friction. Initially the bead is at the middle of the rod and the rod moves translationally in a vertical plane with an acceleration a_(0) in a direction forming angle theta with the horizontal as shown in the given figure. The acceleration of bead with respect to rod is

A bead is arranged to move with constant speed around a loop that lies in a vetical plane. The magnitude of the net force on the bead is

A bead is arranged to move with constant speed around a loop that lies in a vetical plane. The magnitude of the net force on the bead is